Question

Integration by substitution

ive been given this equation

int x^2(x^3-6)^3 dx using u = x^3 -6

but i don't understand how to do it
please help

Answer 1

If in some integration, I see the derivative of the base sitting there either directly or as a multiple, the integration becomes routine.

so intgr x^2(x^3 - 6)^3
= x^2/(4(3x^2))(x^3 - 6)^4 + c
= (1/12)(x^3 - 6)^4 + c

check it by differentiating, it works.